Discrete analytical hyperplanes
Graphical Models and Image Processing
Periodic graphs and connectivity of the rational digital hyperplanes
Theoretical Computer Science
Connectivity of discrete planes
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Discrete Applied Mathematics
On the connectedness of rational arithmetic discrete hyperplanes
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Arithmetic discrete planes are quasicrystals
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
On the connecting thickness of arithmetical discrete planes
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Introduction to digital level layers
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
About thin arithmetic discrete planes
Theoretical Computer Science
Critical connectedness of thin arithmetical discrete planes
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Concurrency relations between digital planes
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector n, we provide algorithms either to determine whether a given arithmetic discrete plane with n as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector n is connected.